Square Root of 2/3
2026-02-28 06:12 Diff
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Last updated on August 5, 2025

If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 2/3.

What is the Square Root of 2/3?

The square root is the inverse of the square of the number. 2/3 is not a perfect square. The square root of 2/3 is expressed in both radical and exponential form. In the radical form, it is expressed as √(2/3), whereas (2/3)^(1/2) in the exponential form. √(2/3) ≈ 0.8165, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 2/3

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the decimal approximation method and simplification method are used. Let us now learn the following methods:

  • Decimal approximation method
  • Simplification method

Square Root of 2/3 by Decimal Approximation Method

The decimal approximation method is particularly used for non-perfect square numbers. In this method, we calculate the decimal value of the square root using a calculator or approximation techniques.

Step 1: Convert the fraction to a decimal. 2/3 ≈ 0.6667.

Step 2: Find the square root of the decimal. √0.6667 ≈ 0.8165.

Therefore, the square root of 2/3 is approximately 0.8165.

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Square Root of 2/3 by Simplification Method

The simplification method involves rewriting the square root of a fraction in a simplified radical form.

Step 1: Express the square root of 2/3 as a fraction under a radical: √(2/3) = √2/√3.

Step 2: Rationalize the denominator by multiplying the numerator and the denominator by √3: (√2/√3) × (√3/√3) = √6/3.

Therefore, √(2/3) = √6/3, which is the simplified form.

Common Mistakes and How to Avoid Them in the Square Root of 2/3

Students often make mistakes while finding the square root, like forgetting about the negative square root or improper simplification. Here are a few mistakes that students tend to make in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(2/3)?

Okay, lets begin

The area of the square is approximately 0.6667 square units.

Explanation

The area of the square = side².

The side length is given as √(2/3).

Area of the square = (√(2/3))² = 2/3 ≈ 0.6667.

Therefore, the area of the square box is approximately 0.6667 square units.

Well explained 👍

Problem 2

A rectangle has a length of 2√(2/3) units and a width of 3 units. What is the area of the rectangle?

Okay, lets begin

The area of the rectangle is approximately 3.265 square units.

Explanation

Area of the rectangle = length × width.

Length = 2√(2/3) ≈ 2 × 0.8165 ≈ 1.633 units.

Width = 3 units. Area = 1.633 × 3 ≈ 4.899.

Therefore, the area of the rectangle is approximately 4.899 square units.

Well explained 👍

Problem 3

Calculate √(2/3) x 4.

Okay, lets begin

Approximately 3.266.

Explanation

The first step is to find the square root of 2/3, which is approximately 0.8165.

The second step is to multiply 0.8165 by 4.

So 0.8165 × 4 ≈ 3.266.

Well explained 👍

Problem 4

What will be the square root of (2/3) × 9?

Okay, lets begin

The square root is approximately 2.121.

Explanation

To find the square root, first calculate (2/3) × 9 = 6.

Then, √6 ≈ 2.121.

Therefore, the square root of (2/3) × 9 is approximately ±2.121.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(2/3) units and the width ‘w’ is 5 units.

Okay, lets begin

The perimeter of the rectangle is approximately 11.633 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Length = √(2/3) ≈ 0.8165 units.

Width = 5 units. Perimeter = 2 × (0.8165 + 5) = 2 × 5.8165 ≈ 11.633 units.

Well explained 👍

FAQ on Square Root of 2/3

1.What is √(2/3) in its simplest form?

2.Is 2/3 a perfect square?

No, 2/3 is not a perfect square, as its square root is an irrational number.

3.How do you rationalize √(2/3)?

To rationalize √(2/3), multiply the numerator and the denominator by √3 to get √6/3.

4.What type of number is √(2/3)?

√(2/3) is an irrational number because it cannot be expressed as a simple fraction.

5.Is √(2/3) a rational number?

No, √(2/3) is an irrational number because it does not terminate or repeat.

Important Glossaries for the Square Root of 2/3

  • Square root: A square root is the inverse of a square. For example, 4² = 16, and the inverse of the square is the square root, that is, √16 = 4.
  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
  • Rationalization: The process of eliminating radicals from the denominator of a fraction.
  • Decimal approximation: An approximate value of a number represented in decimal form, often used for irrational numbers.
  • Fraction: A numerical quantity that is not a whole number, represented by two numbers divided by a slash, such as 2/3.

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.